Arbitrage in a discrete version of the Wick-fractional Black–Scholes market

We consider binary market models based on the discrete Wick product instead of the pathwise product and provide a sufficient criterion for the existence of an arbitrage. This arbitrage is explicitly constructed in the class of self-financing one-step buy-and-hold strategies, (i.e., the investor holds shares of the stock only at one time step). Using coefficients obtained from an approximation of a fractional Brownian motion with Hurst parameter ½<H<1 the result is applied to a discrete version of the (Wick-)fractional Black–Scholes market.